Innovation and Natural Resources: A Dynamic Game with Uncertainty

We analyze a dynamic game between a resource-exporting country and an importing country that is seeking to invent a substitute technology. The time of innovation is an uncertain function of the importer's R&D efforts, which cannot be committed in advance. The game has a unique equilibrium in Markov strategies. The importer's R&D efforts grow over time. The exporter's output often decreases with time before innovation occurs, but strategic factors imply that the opposite can happen. The output path is characterized by a simple modification of Hotelling's rule to account for uncertainty and strategic behavior.